Distance Dependence of the Energy Transfer Mechanism in ${\mathrm{WS}}_2$-Graphene Heterostructures

We report on the mechanism of energy transfer in Van der Waals heterostructures of the two-dimensional semiconductor ${\mathrm{WS}}_2$ and graphene with varying interlayer distances, achieved through spacer layers of hexagonal boron nitride ($h$-BN). We record photoluminescence and reflection spectra at interlayer distances between 0.5 and 5.8 nm ($0–16h$-BN layers). We find that the energy transfer is dominated by states outside the light cone, indicative of a Förster transfer process, with an additional contribution from a Dexter process at 0.5 nm interlayer distance. We find that the measured dependence of the luminescence intensity on interlayer distances above 1 nm can be quantitatively described using recently reported values of the Förster transfer rates of thermalized charge carriers. At smaller interlayer distances, the experimentally observed transfer rates exceed the predictions and, furthermore, depend on excess energy as well as on excitation density. Since the transfer probability of the Förster mechanism depends on the momentum of electron-hole pairs, we conclude that, at these distances, the transfer is driven by nonrelaxed charge carrier distributions.

Figure 1

(a) Sketch of the ${\mathrm{WS}}_2$-graphene heterostructures used in this study. Both materials are separated by spacers of $n$ layers (nLs) of $h$-BN. (b) Photoluminescence image of a ${\mathrm{WS}}_2$-graphene heterostructure with $0-2h$-BN spacer layers. The photoluminescence intensity varies by approximately 1 and 2 orders of magnitude, respectively. (c) Sketch of the competing electronic processes: after excitation, electrons and holes can either recombine radiatively within ${\mathrm{WS}}_2$ or transfer to graphene where they recombine nonradiatively. The relative efficiency of both processes determines the brightness of the emitted light from ${\mathrm{WS}}_2$.

Figure 2

(a) PL spectra of three regions of a sample containing 0–2 layers of $h$-BN as spacers. (b) Reflection contrast (RC) spectra from the same areas as in (a) (offset vertically for clarity). (c) Minimal PL and RC linewidth at room temperature as a function of spacer layer thickness derived from all positions on all samples. (d) Minimal PL linewidth at small interlayer distances, obtained from one sample at 4 K, at which phonon-related broadening is reduced. An increase of the linewidth of $(0.7\pm 0.3)\mathrm{meV}$ is observed for zero spacer layers.

Figure 3

Dependence of the PL intensity on ${\mathrm{WS}}_2$-graphene interlayer distance (green data points). The purple solid line is derived from the predicted Förster energy transfer rates at room temperature [23] by varying the effective radiative rate to best reproduce the data above 1 nm interlayer distance. The dashed black line additionally includes the experimentally obtained Dexter term. The individual rates underlying the models are shown in the inset.

Figure 4

(a) Calculated broadening due to Förster energy transfer as a function of momentum transfer $Q$ for different interlayer distances. Bottom: Boltzmann distribution at 295 K and maximum available momenta for cw excitation with a 532 nm laser (green) and a 594 nm laser (yellow). (b) Photoluminescence intensity in areas of 0–2 spacer layers for an excitation wavelength of 532 nm (green) and 594 nm (yellow). (c) Power dependence of the PL intensity for 0–2 spacer layers. The dashed gray lines indicate a linear increase.